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Impact of fear effect on plankton-fish system dynamics incorporating zooplankton refuge

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  • Kaur, Rajinder Pal
  • Sharma, Amit
  • Sharma, Anuj Kumar

Abstract

In this paper, we analyze the impact of anti-predator behavior due to fear effect (K) and zooplankton refuge (r1) on a 3-D plankton-fish dynamical system involving phytoplankton, zooplankton, and fish species. We assume that zooplankton species have developed defense mechanisms against fish predation. The fear of fish predation altered anti-predator defenses, which affects the growth of the fish population. On the other hand, zooplankton refuge reduces fish induced mortality of zooplankton and plays a significant role in controlling phytoplankton growth. The density of fish species is suppressed in the presence of high refuge and the anti-predator response of zooplankton. It is determined that K and r1 can influence not only plankton-fish demography but also induce some mechanism to terminate planktonic blooms. Our mathematical study reveals that the low level of fear can stabilize the system dynamics in the presence of high rate of zooplankton refuge. Moreover, the low rate of zooplankton refuge can exclude complexity from the plankton-fish ecosystem in the presence of strong anti-predator responses of zooplankton. We have established the existence of all feasible biological equilibria and derived the conditional local and global stability of the given system around it. The Hopf-bifurcation analysis is carried out by considering K and r1 as bifurcation parameters. The direction of bifurcating solutions is also determined using the centre manifold arguments. Numerical simulation is carried out to substantiate our analytical findings.

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  • Kaur, Rajinder Pal & Sharma, Amit & Sharma, Anuj Kumar, 2021. "Impact of fear effect on plankton-fish system dynamics incorporating zooplankton refuge," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309541
    DOI: 10.1016/j.chaos.2020.110563
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    1. Fangyuan Hua & Kathryn E. Sieving & Robert J. Fletcher & Chloe A. Wright, 2014. "Increased perception of predation risk to adults and offspring alters avian reproductive strategy and performance," Behavioral Ecology, International Society for Behavioral Ecology, vol. 25(3), pages 509-519.
    2. Sönke Eggers & Michael Griesser & Jan Ekman, 2005. "Predator-induced plasticity in nest visitation rates in the Siberian jay (Perisoreus infaustus)," Behavioral Ecology, International Society for Behavioral Ecology, vol. 16(1), pages 309-315, January.
    3. Zhang, Huisen & Cai, Yongli & Fu, Shengmao & Wang, Weiming, 2019. "Impact of the fear effect in a prey-predator model incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 328-337.
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    Cited by:

    1. Yuke Zhang & Xinzhu Meng, 2022. "Dynamics Analysis of a Predator–Prey Model with Hunting Cooperative and Nonlinear Stochastic Disturbance," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    2. Sajan, & Dubey, Balram & Sasmal, Sourav Kumar, 2022. "Chaotic dynamics of a plankton-fish system with fear and its carry over effects in the presence of a discrete delay," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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